How to cut a piece off a mesh using another mesh/edge as the cut shape
I’ve run into this type of problem before. I recommend extruding the circular background, and then using the resulting edge-to-faces to cut the wave tube. You may have to move the circular background a bit to make it offset, so it doesn’t just cut half the tube.
Use Boolean or the Boolean modifier for cutting. Selecting the mesh to be cut (I think, maybe it’s the other way around and you select only the mesh that’s DOING the cutting)